Elastic‐Plastic‐Softening Analysis of Plane Frames

Abstract

Softening of reinforced concrete sections at advanced curvatures in flexure is taken into account in collapse load analysis of frames. The analysis employs a trilinear elastic‐plastic‐softening approximation to real moment‐curvature curves, and elastic unloading and reloading from the softening curve is assumed. Formulas for hinge length in reinforced concrete flexural members are reviewed. Elements of a stiffness matrix for elastic elements with softening portions are derived. The stiffness matrix allows extension of the capability of an existing computer program for elastic‐plastic analysis to softening or hardening. Several examples demonstrate the application of computer program PAWS (Plastic Analysis with Softening) to concrete frame structures. A steeper softening slope reduces both the number of hinges formed before collapse and the collapse load, compared with elastic‐plastic behavior. Values of critical softening parameters for first or later formed hinges may be found using PAWS, and theoretical values are confirmed. Quite small softening parameters lead to large reductions in static collapse and shakedown loads, especially when there are significant residual moments.